ACR MLG SIGHTED WRONG ACFT INSTRUCTED TO FOLLOW ON VISUAL APCH.

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DEPARTED SLI VOR 320 DEGS HDG AT 7000' MSL. SLOWED TO 180 KTS AND TURNED TO 020 DEG HDG BY ATC. FURTHER AIRSPD REDUCTION TO 170 KTS. ASKED BY APCH IF WE HAD TFC AT 11 O'CLOCK IN SIGHT. WE HAD ONE AT 8-9 O'CLOCK AND ONE AT 12 O'CLOCK. RPTED 12 O'CLOCK TFC IN SIGHT. WE WERE THEN CLRED FOR A VISUAL APCH BEHIND THAT TFC FOR RWY 25R. I ASKED THE F/O TO VERIFY WHICH ACFT WE WERE TO FOLLOW. F/O COULDN'T GET INTO ATC DUE TO FREQ CONGESTION. CONTINUED ON 020 DEG HDG TO FOLLOW THE 12 O'CLOCK TFC; BUT STILL WEREN'T SURE IF IT WAS CORRECT TFC TO FOLLOW. FINALLY GOT APCH TO VERIFY AND HE ADVISED US THAT WE SHOULD HAVE TURNED SOONER (TO FOLLOW TFC THAT HAD ORIGINALLY BEEN AT OUR 8-9 O'CLOCK POS). STARTED TURN TO 260 DEGS AND DSCNT PER ATC. AT ABOUT 6600' MSL IN DSCNT CTLR CHANGED INSTRUCTIONS TO TURN TO 210 DEG HDG AND MAINTAIN 7000' FOR RESEQUENCE. WE COMPLIED AND WERE VECTORED AROUND FOR ANOTHER VISUAL APCH. PROBS WERE: INABILITY TO POSITIVELY IDENT ACFT WE WERE TO FOLLOW; FREQ CONGESTION PREVENTED VERIFICATION SOONER AND ATC WORKLOAD EXTREMELY HIGH. CORRECTIONS: BOTH CTLR AND CREW SHOULD BE POSITIVELY SURE OF TFC BEFORE VISUAL APCH IS ISSUED AND; ALT OF ACFT TO BE FOLLOWED; IN DSCNT OR LEVEL FLT; SHOULD ALWAYS BE GIVEN. THE TFC AT OUR 8-9 O'CLOCK WAS CONSIDERABLY LOWER THAN THE TFC AT 12 O'CLOCK AND THIS WOULD HAVE ALERTED US SOONER AND PREVENTED OR HELPED TO PREVENT LOOKING AT THE WRONG ACFT.